Convert a = 60o to a Car Oy = x/2 Ox = V3y Oy= V3x

Q: Convert the polar equation r² = 2tan 0 to a Cartesian equation. x3 + y3 = 2 y x3 + xy² = 2 y x² + y²…

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Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

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Q: Write an equation of the plane with normal vector n= (2,8, -4) passing through the point (3,-9,-5)…

A: Vector equation of plane is used.

Q: Convert the Cartesian equation x 2 + y 2 - 6x = 0 to a polar equation.  r² = 6cosθ r = 6sinθ r =…

A: The given Cartesian equation x 2 + y 2 - 6x = 0 ................................... (1)

Q: y = 2Vx, y= Find the area of the region enclosed by the curves.

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Q: Find f. f "(x) = 1//1- x?, () - = 2 f(x) =

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Q: Find each limit: 3x2 - 2x + 2 A) lim 11x? - 8x 9. T 00 B) lim エ 0 12x + 8 C) lim 8x2 + 3x 7

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Q: Consider the function 70 - 3 f(x) = 22 — 2х — 63 Find the vertical asymptotes of f(x). Separate…

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Q: Evaluate the definite integral. 13 i+ej+t k dt O e13 – 1 -(61 -1) + 1 13 e13 i- (e- - 1) j+ 1 13 2…

A: We have to find the integral

Q: Consider the following curve. f(x) = Vx2 + 2x - x Determine the domain of the curve. (Enter your…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: For the function f(x) = x ln(1+ x°), %3D a) What is the Maclaurin series for f and its interval of…

A: Given function is fx=xln1+x3Maclaurin Series of function fx…

Q: 1) Sketch the curve. a) r=-2 sin O Show All Work

A: Here we have to sketch the given curve.

Q: Find the dy/dx by implicit differentiation. 1. 4x2 – 9y2 = 1 2. x³ + y3 = 8xy 3. x? – 7xy + y2 = 0 |

A: As we know that; The sum/difference rule: f±g'=f'±g' The Power law; ddxxn=nxn-1 The Product rule:…

Q: Construct the following rational functions. a. Construct a rational function whose only asymptotes…

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Q: In a study of children, a total of 1,560 children were examined. Of these, 1,018 had rickets. Of the…

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Q: dx J (x² + 2x – 10)²

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Q: #13-Find the cost function for the morginad cost fixed cost of $6000 (for x -0) O** 70 X*-80 and

A: cost function = ∫ (dc/dx)dx cost function = ∫ x2/70 + 80dx cost function = x3/210 + 80x + k lets put…

Q: Find the differential of the given functions: 1. y = 3x4 - 5x³ + x - 4 2. u = /2y – y3

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Q: Find the equation of the following hyperbola. Express your answer in standard form. Enable Zoom/Pan…

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Q: 29,4 15.4 82.6 A graph of f is shown above. The numbers shown represent the geometric area of each…

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost…

Q: Q2. Let a card be selected at random from an ordinary deck of 52 cards Let A = [ the card is a black…

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Q: | 4x sech x2 tanh x2 dx A) - 2 sech x² + C (в) 2 B sech x2 + C sech x2 +C C 2x D) 4 csch x2 + C

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Q: 1(x) (х+1)* II

A: follow the procedure given below.

Q: Find the volume of the solid that results when the region enclosed by 7x 0, х — 8, and Y : 0 is…

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Q: 4. (i) Use the parametric equations of an ellipse, z = a cos (t) , y = bsin (t), 0 < t< 2r, to find…

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Q: ASSIGNEMNT #5 Determine if the function is continuous on the indicated close interval SVx +1 (5- x 0…

A: A function y=f(x) is said to be continuous at x=a iff, limx→a-f(x)=limx→a+f(x)

Q: M. Vx? N. xe* O. 4 Р. cot x Q. cot?x R. 2 cot x

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Q: Given D (4, 2) = 5, fwm (4, 2) = 8, we know that (4,2) is a minimum we cannot tell O saddle point…

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Q: x =r' +1, y=r -t d'y d’y b) Find dx?

A: Given: x=t3+1 and y=t2-1

Q: Evaluate the following integral: •Vx+4 sin(y – 3y?) dy Jx+4 | 2

A: First we integrate the given function and then we put limit and simplify.

Q: 19. Evaluate the given integral, ſe*1+ ex dx: A.(1 + e*) + c B. (1 + e*)} + e c. (1 + e*)* + D. (1+…

A: Evaluate the given integral,

Q: Find the points on the ellipse 3x2 + y2 = 3 that are farthest away from the point (1, 0). What I…

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Q: For f(x,y)=-6x'y° : (a) Determine fx(x,y) . 6.6 Answer: -42x (b) Determine fy(x,y). Answer: -36x 7.5…

A: Given query is to find the Indicated derivative.

Q: The x-intercepts of f(x)=x°+ 11x²+ 10x are: %3D O a. (0,0), (1,0) and (10,0) O b. None O c. (-1,0)…

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 4cscθ

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Q: Q2. Let a card be selected at random from an ordinary deck of 52 cards. Let A = [ the card is a…

A: From given information,  n(S)=52, n(A)=6, n(B)=26

Q: x² +1, if x-1 odd f(x)= ,2_1. if x+1 even Find the value of f(1)+ f(2)+f(3). O a. None O b. 12 О с.…

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Q: Scot'x csc'xdx 4.

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Q: 4. Determine the general equation of the plane containing the points P(1, –4, –5), 3 Q(2,0, 13) and…

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Q: If g(t) = 2t* + 3t2 - 5 find g(0) = a'(0)

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Q: Assume the annual rate of change in the national debt of a country (in billions of dollars per year)…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: What would be the shape of the graph r = 2 cos 0, given that 0 = 0, 7 , 5, 5? O semi-circle in the…

A: We know cosθ takes positive values in first quadrant that is for 0&lt;=θ&lt;=π/2 The equation…

Q: What is a total weight of 7 basketball that weight 22 ounces each

A: Given each basketball weight is 22 ounces

Q: Find an equation of the plane through the three points given: P = (0,0, 5), Q = (-4, 2,2), R = (-1,…

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Q: Convert the polar coordinates (4, 315) to Cartesian coordinates. (2√3, -2) (2√2, -2√2) (2, -2√3)

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Q: y = (1+) - (1+)*

A: We have to find dy/dx for the given function.

Q: 2. Use the Simpson's (1/3 c2 (c) x sin x dx

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Q: Verify that the vectors a = (2, 5, –1) and b = (3, –1, 1) perpendicular. а. are

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Q: 4. Sketch the function Ax) = 2xª – 16x², indicating any extrema, points of inflection,

A: follows the procedure given below.